Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The crossed product of a $ C\sp{\ast} $-algebra by an endomorphism


Author: William L. Paschke
Journal: Proc. Amer. Math. Soc. 80 (1980), 113-118
MSC: Primary 46L05; Secondary 46L55
DOI: https://doi.org/10.1090/S0002-9939-1980-0574518-2
MathSciNet review: 574518
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let A be a unital, strongly amenable $ {C^ \ast }$-algebra, $ \sigma :A \to pAp$ a $ ^ \ast $-isomorphism (where p is a proper projection of A), and S an isometry such that $ Sx{S^ \ast } = \sigma (x)$ for all x in A. If A has no nontrivial $ \sigma $-invariant ideals, then $ {C^ \ast }(A,S)$ is simple. Furthermore, $ {C^\ast}(A,S)$ is isomorphic to a corner of the crossed product of $ A \otimes $ (compacts) by an automorphism.


References [Enhancements On Off] (What's this?)

  • [1] L. G. Brown, Stable isomorphism of hereditary subalgebras of $ {C^\ast}$-algebras, Pacific J. Math. 71 (1977), 335-348. MR 0454645 (56:12894)
  • [2] J. Bunce, Representations of strongly amenable $ {C^\ast}$-algebras, Proc. Amer. Math. Soc. 32 (1972), 241-246. MR 0295091 (45:4159)
  • [3] J. Bunce and W. L. Paschke, Quasi-expectations and amenable von Neumann algebras, Proc. Amer. Math. Soc. 71 (1978), 232-236. MR 0482252 (58:2330)
  • [4] A. Connes, On the cohomology of operator algebras, J. Functional Analysis 28 (1978), 248-253. MR 0493383 (58:12407)
  • [5] J. Cuntz, Simple $ {C^\ast}$-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173-185. MR 0467330 (57:7189)
  • [6] J. Cuntz and G. K. Pedersen, Equivalence and KMS states on $ {C^\ast}$-dynamical systems, preprint, 1978.
  • [7] M. M. Day, Normed linear spaces, Springer-Verlag, Berlin, 1962.
  • [8] D. Olesen and G. K. Pedersen, Some $ {C^\ast}$-dynamical systems with a single KMS state, Math. Scand. 42 (1978), 111-118. MR 500150 (80a:46041)
  • [9] J. Rosenberg, Amenability of crossed products of $ {C^\ast}$-algebras, Comm. Math. Phys. 57 (1977), 187-191. MR 0467331 (57:7190)
  • [10] -, Appendix to O. Bratteli's paper on ``Crossed products of UHF algebras", Duke Math. J. 46 (1979), 25-26. MR 523599 (82a:46064)
  • [11] H. Takai, On a duality for crossed products of $ {C^\ast}$-algebras, J. Functional Analysis 19 (1975), 25-39. MR 0365160 (51:1413)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 46L55

Retrieve articles in all journals with MSC: 46L05, 46L55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0574518-2
Keywords: $ {C^ \ast }$-algebra, crossed product, simple
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society